Henrietta Maria's marriage contract gave her full control over the education and religion of any children she might have with her husband, until the children were aged eleven. This condition was not honored, however, which made Henrietta very angry.
Charles may well have told Henrietta that she could have full control over their youngest child, including her religion, but Charles often told people what they wanted to hear.
It is true that Charles did not leave specific directions for Minette's religion, aside from having her baptised in the Anglican faith, but at the time of his execution in 1649, he fully believed that his son and namesake, as well as the rest of the family, would be returning to England and reinstated. Charles may not have believed leaving such instructions was necessary, since he had told his son and namesake, over and over, about the importance of the Anglican religion. If Charles had wanted to make an exception for Minette, he would have gotten word to Charles II. Throughout his captivity, Charles sent letters and messages to Charles II and his other children, admittedly not Minette, to stay true to the Anglican religion. Just before he was executed, Charles met with his children Elizabeth and Henry, and urged them to remain true to the Anglican faith, even recommending books to read.
Until he was thirteen, Charles had been brought up to be a bishop; he received a thorough grounding in the Anglican religion. I believe that Charles would not have approved of Minette becoming a Catholic, no matter what he said or wrote to Henrietta to the contrary. I believe Charles counted on his son and namesake to keep the family Anglican. It is unfortunate that the Interregnum lasted eleven years, instead of the months Charles evidently foresaw.
The problem with Minette, as umigon pointed out, was that she did not have a good education. She was not used to the French Court, or any other Court; there was some belief before her marriage that Minette would become a nun, and if Charles II's restoration had taken a few years longer to achieve, I think that is what would have happened. Henrietta Maria simply did not prepare Minette to play a public role, though Henrietta did encourage Minette to dabble in politics after her marriage, for Charles II's sake. I think she was in over her head from the beginning. It is unfortunate that Minette did not spend a few years at the Court of Charles II in London before her marriage. She brought out the best in Charles II, and he might have helped her learn to discern between flattery and true friendship, etc.
I really don't think Minette gave Philippe much of a chance when they married, and he was quick to find refuge with his boyfriends, some of whom were indeed nasty characters. Philippe's boyfriends undoubtedly encouraged the estrangement between Philippe and Minette. The legend that one of his boyfriends had Minette poisoned, however, is ridiculous. There can be little doubt that Philippe's circle of friends and boyfriends hated Minette, and tried to get her in trouble with Louis XIV and Philippe, but she wasn't an innocent victim either. Minette caused problems for herself which Philippe's circle exploited.
It is true that there are no eyewitness reports about Minette's affairs. However, it is also true that her biographers rely largely on the memoirs of Madame de Lafayette, who was eager, particularly after Minette's tragic death, to paint her in a good light. I have difficulty believing that there was that much smoke without fire where Minette and her love life were concerned, having plowed through many of the Memoirs of that era.
All of this is just my opinion, and your mileage may vary.